Re: [tuning] Re: vealing Structure for dkeenanuqnetau

You are very right
the scale was constructed in the opposite way you describe as a sort of
mathematical joke
you identify the proper scale immediately and i am so glad you made the
wonderful suggestions in regard to teh major 7 pitch.
i will add your two replacement scales to the f-tables andsend you some
examples if you would like.
Mr. Keenan...did'nt you figure this scale out before??
Well we must tell MOnzo
and can we call this scales(s) you suggest
"pagano/beardsley scale-the keenan variations"
1 an 1a respectively

give me a day of two to subject them to the random engines and i will see
what i can generate
musically

Pat Pagano, Director
South East Just Intonation Society
http://www.screwmusicforever.com/SHREESWIFT/
----- Original Message -----
From: dkeenanuqnetau <d.keenan@uq.net.au>
To: <tuning@yahoogroups.com>
Sent: Friday, March 22, 2002 12:24 AM
Subject: [tuning] Re: Pat Pagano @ Csounds.com !!!!!!!!!!!!!!!!!!!!!!!!

> --- In tuning@y..., "shreeswifty" <ppagano@b...> wrote:
> > Dear Friends
> > Hans Mikelson has graciously included me in his fabulous Csound
> Magazine
> > http://csounds.com/ezine/cgspframe.html
> > Let me know what you think
> > Cheers!
> >
> > Pat Pagano, Director
> > South East Just Intonation Society
> > http://www.screwmusicforever.com/SHREESWIFT/
>
> Hi Pat,
>
> Congratulations on getting published. I thoroughly enjoyed the piece.
>
> That scale
>
> 1/1 17/16 425/384 153/128 51/40 1377/1024 17/12 119/80 51/32 17/10
> 85/48 119/64 2/1
>
> makes a lot more sense if you transpose it so the 17/16 becomes the
> 1/1. I'm not saying you should treat the 17/16 as the tonic (but do
> you actually treat the 1/1 as a tonic anyway?), just that recasting
> the scale in this way reveals its structure. It is then seen to be
>
> 1/1 25/24 9/8 6/5 81/64 4/3 7/5 3/2 8/5 5/3 7/4 32/17 2/1
>
> The 32/17 can then be seen as being "tempered by ratios" about halfway
> between 243/128 (a 2:3 above 81/64) and 15/8 (a 4:5 above 3/2).
>
> It's certainly a rational scale, and one could even call it a
> Just-but-for-one-note scale, but I don't think it's quite correct to
> call it simply a Just scale because there's no way you could tune the
> 32/17 (the original 1/1) by ear against any combination of the other
> notes (except with a purpose-built timbre having a lot more 17th
> harmonic than anything other). I claim that its precise tuning doesn't
> really matter so long as it is somewhere near halfway between those
> two pitches I mentioned which are a syntonic comma apart.
>
> If you want to prove me wrong, you could try 17/9 or 49/26 or 66/35
> instead of 32/17. The original scale would become respectively
>
> 1/1 18/17 75/68 81/68 108/85 729/544 24/17 126/85 27/17 144/85 30/17
> 63/34 2/1
> or
> 1/1 52/49 325/294 117/98 312/245 1053/784 208/147 52/35 78/49 416/245
> 260/147 13/7 2/1
> or
> 1/1 35/33 875/792 105/88 14/11 945/704 140/99 49/33 35/22 56/33 175/99
> 245/132
>
> I predict that these will be indistinguishable from your original
> scale in normal use, e.g. in the abovementioned enjoyable piece.
>
>
>
>
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